with the probability taken over \((Y^{n+1}, W_{n+1})\)  now, which implies that exact coverage probability for the corresponding randomized prediction plausibility region. One will also immediately recognize \(\pi ^{w_{n+1}}(y_{n+1}; y^n)\)  as conformal prediction's “smoothed p-value” in, e.g., Equation (2.20) of [1]}.
